CALL IT QUITS
NY Times Crossword
October 16, 2013
Samuel A. Donaldson (adapted)

The same three-letter word can change the following words into new ones:

TORY
PANIC

The same four-letter word can change the following words into new ones:

FAT
ELF

Both the three-letter word and the four-letter word are the same grammatical part of speech.

A common four-word expression, which means the same thing as the title of this puzzle, gives the key to the solution.

Answers:

TORY and PANIC can be changed by adding HIS.
FAT and ELF can be changed by adding HERS. 

Both words are possessive pronouns.

The expression that solves the puzzle is THROW IN THE TOWEL (as in HIS and HERS towels) - which means to CALL IT QUITS.