According to TULIP Calvinism grace is "irresistible". If grace is irresistible then what role does faith play in salvation and can it still be considered a gift?
Yes, salvation can still be considered a gift. In general, something can be considered a gift if it:
Whether a gift can be resisted or not has no bearing on its "giftiness". According to Calvinism, faith comes into play as the mode with which we receive the gift of salvation. So, in order to cause us to be saved, God regenerates us and then causes us to have faith.
The irresistible quality of the process (regeneration and subsequent faith) does not undermine it's "giftiness". On the contrary. According to Calvinism, salvation would not be purely a gift if it were resistible, because then the act of choosing to not resist the gift could be construed as meritoriously earning it, at least in part.
It seems the answers here created this question.
In Calvinism the grace is that God gives you faith, which then saves you.
You are elected to receive that grace without condition. Nothing you do, could do, have done, or anything to do with you or your actions was weighed in determining your election. That is why is is called unconditional election.
That is the very definition of a gift. You are receiving something that you do not deserve, nor did you earn, nor will you have to do anything to keep it. You were elected to receive the gift of faith through the grace of God.
Because that grace is irresistible is irrelevant to the fact that is is still a gift that you did not deserve. What you did deserve is death and hellfire. Instead God has poured out His grace on you, which gave you the faith to believe. You have then been saved by faith through His irresistible grace.
To clarify things, here is the chronology of events: