There is no creature more closely associated with death, destruction, and man-killing in Indo-European thought than the wolf/dog. So it is not at all surprising that we should find Tiw, whose best (surviving) association is martial in nature, so closely associated with the wolf.
According to the Prose Edda only Tiw was brave enough to feed the Fenriswulf (Wolf of the Fens), and so earned the by-name “Feeder of the Wolf“; which no more means, simply, that Tiw regularly poured out the kibble-and-bits then the poetic kenning “feed the ravens” meant that a warrior was going out to sit on a bench in the local park and scatter seed for the birds. In both cases the kenning is based upon observed behaviors of the raven and the wolf in relation to the battlefield, and their natures as carrion creatures, as eaters of the dead.
And so, as with “to feed the raven”, the notion of “feeding the wolf”, meant to engage in man-killing, to make war.
This is the function of the warrior and god of war… to kill the enemy, and to thereby feed both wolf and raven.
The same poeticism is — not surprisingly given the overtly poetic nature of our sources, not to mention the chief god of our pantheon — to be found in Tiw’s other by-name, the Leavings of the Wolf, which does not refer, simply, “to everything but Tiw’s hand (which the Wolf bit off)”, but rather to what is left of a man after the wolf of death, the wolf of the grave, has had its fill. These connotations to the Fenriswulf are clear and evident in his siblings (Hell, the Wyrm), whose birth and relation form the background of the “binding of the Fenriswulf” myth as we have it from Snorri.
And what is left of a man after the wolf of the grave has had its fill is spelt out throughout the heroic poetry of our ancestors, ie. the name undying, but perhaps most memorably represented in the most well-known of the Havamal verse, “Cattle die, kinsmen die, and so shall you yourself, but I know one thing that never dies, the praise of one’s worthy deeds.”
That the “Leavings of the Wolf” is a kenning for glory is seen in Snorri’s reference to the use of his name (Tyr) in reference to men of exceptional boldness (and wisdom), in its poetic use in praise of warrior-kings, and in its ancient usage as a general word for any deity individually, and of all the deities collectively.
The root of this word/name traces back to the same root that gave us various words for the sky and day, as well as the names of various (ahem) “skyfathers” (eg. Zeus) including the prototypical Skyfather (ie. Dyauspita). And so at the root of the notion of (ahem) “god” as manifest in the word tiv and its Indo-European cognates, and which distinguishes it from any of the host of other words that also “mean god”, such as the word god itself for example (but also regin, vear, aesir, etc.) is the notion of “heavenly radiance”.
The line between godhood, that is tiv-hood, and glory, is clearly a very fine matter in the lore. In Sanskrit, this same word (deva) can refer to anything of excellence.
So, warfare. And death and glory. But not necessarily glory, the achievement of excellence, in regards to war alone as the association with knowledge and wisdom might indicate.
However, in Tiw’s association with the wolf, which dates at least back to the Vendel period as evidenced in at least three of the bracteates of the era, we see nothing that is not paralleled in Woden’s Eddic relationship with the wolf. In the Griminsmal for example we read that Woden feeds his wolves great chunks of meat, but that he sustains himself on wine alone… the great chunks of meat referencing the bodies of the battle-slain while the wine (of memory and toasting) references the heroic glory of the battle-slain.
It is as much on this point — ie. the relation of both Tiw and Woden to the wolf and specifically to the Fenriswulf, and to warfare itself, — as in the P.I.E. roots and I-E associations of the name Tiw, that academics theorized that Tiw once occupied a higher position in the sphere of warfare and the pantheon in general.
By the same virtue, others have speculated that Tiw was just another name For Woden.