In The Great Gatsby, Tom is traditional, well-established, conservative, safe in the sense that he is part of society's status quo. But Tom is also abrasive and dominating and even abusive. Gatsby is none of these, as far as the reader knows.
But whatever conflicts the above cause are only secondary in the novel, and only really come into play when Tom uses whatever he can to verbally attack Gatsby, once he knows Gastby has a relationship with Daisy.
Gatsby, new, mysterious, seemingly a man of the world, certainly a self-made man, tries to woo Daisy and recapture the romance he believes they once shared. Tom, domineering, physically powerful, bull-headed, is honestly shocked when he finds out Daisy has become involved with someone outside of their marriage, even though he has been doing the same. And he certainly isn't going to let some outsider come from nowhere and take his wife away.
Whether Tom is awakened by the threat to his marriage or he simply protects what he sees as his and will remain the same type of husband he has been is left ambiguous, but he certainly does come out ahead in his conflict with Gatsby.
To me, the conflict between Tom Buchanan and Jay Gatsby is conflict on two levels. There is conflict because of Daisy, and there is conflict because of the differences in class between the two men.
The first conflict is obvious. The two men both want the same woman. Gatsby wants her for love, Tom, I think, just wants her because she "belongs" to him.
The second conflict is less obvious. It comes about because Tom has "old money" and Gatsby does not. You can see this in how Tom hates Gatsby saying "old sport" (implies he things Gatsby is putting on airs) and how he dislikes the way Gatsby has made his money.