A “super PAC” supporting Hillary Clinton will begin airing ads in New Hampshire and Pennsylvania that tether Donald J. Trump to embattled Republican senators there.

The group, Priorities USA, will run ads in the Manchester, N.H., and Philadelphia markets, as Senators Kelly Ayotte of New Hampshire and Patrick J. Toomey of Pennsylvania face difficult re-election battles.

The move is a new phase for Priorities. Mrs. Clinton’s lead over Mr. Trump has allowed the group to focus on down-ballot races.

This week it will also begin airing television and radio ads in Georgia, a reliably Republican-leaning state that polls show may be in play in the presidential race.