Noble Celtic Wolf Art Solid Brass Wrist Watch Collectible. Golden.

For the 'Celts', we need to distinguish different regions of the Celtic World and different periods, notably between the Continental 'Celts' and the Insular 'Celts', between Antiquity and the post-Roman (medieval / Christian)l period.
In medieval Celtic mythology (i.e. mainly Wales and Ireland, and also Britanny), where ancient myths and legends were written down in a Christianising context, wolves play a number of important roles. Similar to the Roman story of Romulus and Remus, a future king was once again reared by a she-wolf: Cormac mac Airt grew up to become an important High King of Ireland (v. infra).
In many Irish/Welsh myths, the wolf is usually a helper and a guide. We also find myths of deities in wolf form, like the goddess Morrigana appearing in wolf form, but was defeated by the hero Cú Chulainn - the 'Hound [or Wolf?] of Cuainn' (cf. The Táin).
There is also the old Gaelic/Irish month faoilleach, which comes from faol or faol-chù, "wolf", i.e. the "Month of the Wolf", February (in other cultures it is often January: January/February are obviously a period in which wolves may be more present [mating period]).

The pre-medieval 'Celtic World' is of course much larger, covering most of Europe for over one millennium, from the Hallstatt period down to late Antiquity. It is therefore no surprise that wolves probably played a different role in each local myth and local religion, though there might be some common denominator.
Since religious affairs were not written down in ancient times (according to Caesar, in his "Gallic War / de bello Gallico", the druids did not allow this!), our knowledge of ancient Celtic mythology is largely based on iconographic representations in art and on coinage. We are really dealing with a jigsaw puzzle where most of the pieces are lost.
Various objects provide important clues. For example, the wolf does appear on a number of coins in the Iron Age, for example among the Carnutes, but it is difficult to explain his mythical, religious role. See the coins below with a variety of wolf depictions.

In several regions of pre-Roman Europe, the wolf iconography shows similarities to Norse mythology. As shown by Daphne Nash-Briggs (2010; 2017), the wolf seem to have a role similar to the mystical wolves in Norse mythology where the wolves Sköll and Hatti chase the moon and the sun across the sky, and will finally catch up and eat them, and Fenrir is said to kill Odin at Ragnarök at the end of the world (also cf. Green: 1998, 160).
We seem to find depictions of these mythical stories also on Celtic coins. Often we see the wolf, with open mouth, in combination with a number of symbols, frequently depicting the moon and/or the sun. For example, a coin discovered at Saint-Germain-en-Laye depict «le loup mangeur de lune» (Hollard 1999) with the wolf being about to sink his teeth into the «moon» which is depicted as a crescent. Above the wolf, we sometimes find «solar horse»; the latter is often also depicted being chased by a wolf, sometimes a stylised wolf or composite animal (Nash Briggs 2010).
Another, «moon-eating» wolf can be found, for example, on a stater from the Calvados area (3rd-2nd century BC; Nash-Briggs 2010, 2, fig. 1).
The so-called Norfolk Wolf coins, from the territory of the Iceni in eastern Britain, provide a comparable iconography, like a «Norfolk Wolf A» stater (c.  56-53 BC) which shows a stylised wolf about to swallow the moon, represented as a lunar eclipse (Nash Briggs 2010 for discussion; cf. ibd.: Figs. 4, 12, 14). On other coins we fine the wolf, the sun and the moon together with other symbols, like a palm tree, serpent, eagle (e.g. BN no. 6925, from the Unelli; cf. Duval 1989: 385).
But we should not conclude that wolves therefore have negative connotations.

• First, they are clearly not normal wolves, but mystical, divine, gigantic «beasts», like Fenrir, the son of god Loki.
• Second, we seem to be dealing here once again with an etiological myth aiming at explaining not only the movement of the sun and the moon, but also the solar and lunar eclipses. This is of course something that we find in many cultures (cf. Burillo 2017: 269-270, also for the Chinese canine equivalent, tiāngoǔ). In this way, Sköll and Hatti are essential for life on earth since without them the sun and moon would not move.
• Third, the destruction of the world also means its re-birth and renewal (cf. Green 1998: 160). Many mythologies and religions know about the (periodic) destruction of the world and the cosmos and its subsequent re-creation: we find this for example in the Germanic Ragnarök, in Irish mythology (Lajoye 2016: 124-5), in the endless cycle of ἐκπύρωσις in Stoic philosophy (Harrill 2010: 121-2), and we can also refer to comparable scenarios, like the Deluge in many ancient cultures.

See Daphne Nash Briggs (2010), «Reading the images on Iron Age coins: 3. Some cosmic wolves», Chris Rudd List 3/110: 2-4.

For the wolves in Norse mythology, see Wolf Myth Norse section!

There is a lot of literature on 'Celtic' myth and religion, but wolves are rarely discussed. But see for example Miranda Aldhouse-Green, An Archaeology of Images: Iconology and Cosmology in Iron Age and Roman Europe.

A little excursion to the Iberian peninsula where we find populations that are categorised as Celts, Iberians and Celtiberians:

Further Reading on Iberia: for example, Héctor Uroz Rodríguez, Practicas rituales, iconografía vascular y cultura material...

Jorge García Cardiel ('El combate contre el mal', Complutum 25(1), 2014: 159-175) interprets the "wolf" as evil in Iberian iconography. But was this really the case? We really need to scrutinise the evidence for this. In the image of the wolf and the boy, below, are we really dealing with an image of an aristocrat fighting a mythical beast, in form of a wolf, presenting evil (cf. Cardiel 2014)? Or are modern scholars not influenced by their own cultural background, like the demonisation of the wolf in Christianity and in the last centuries in western Europe.
Indeed, we may ask whether we may not be dealing with something quite different? After all, this comes from a period with relatively few proto-urban and urban settlements and a basically agricultural society. Once again, the wolf is likely to symbolise the perfect 'warrior', the instinctive forces of nature, symbolising 'the survival of the fittest'. The wolf is a guide, both in this life and in the afterlife. On the vase painting below we see the boy, the young/future warrior, standing face-to-face with a larger-than-life wolf. This does not represent a fight, especially when we consider the decoration of the entire vessell. Perhaps it shows a rite de passage (or coming-to-age ritual), as we have seen in so many other cultures (see e.g., José Carolos Fernandéz). We also should not forget the wolf's role as teacher, here perhaps for good hunting.

Celtic Ireland: Let's go back to Medieval Ireland. In Geralde de Barri's Topographia Hibernica (MS. Roy 13B.viii) from the 13th century AD), we find a story that has some resemblance to wolf myths in other cultures: humans turning to wolves for a certain period as well as wolves showing travellers the right way.
The story tells of a priest travelling from Ulster to Meath in AD1182 who met a talking wolf. He told the priest that he came from Ossory (kingdom / diocese around Kilkenny), "on whose race lay an ancient curse whereby every seven years a man and a woman were transformed into wolves; at the end of seven years they recovered their proper form, and two other suffered a like transformation. He and his wife were the present victims of the course; his wife was at the point of death, and he prayed the priest to come and give her the viaticum' (i.e. the last rites / Holy Eucharist). The priest did it and the grateful wolf showed the priest the right road to Meath (cf. J.R. Green, Short history of the English People, II, London 1908, lxix-lxxx).