President primarily in America for the good times (3)
I believe the answer is:
ups
'the good times' is the definition.
(as in 'ups and downs')
'president primarily in america' is the wordplay.
'primarily' says to take the initial letters.
'in' indicates putting letters inside.
'america' becomes 'us' (United States).
The first letter of 'president' is 'p'.
'p' put into 'us' is 'UPS'.
'for' acts as a link.
(Other definitions for ups that I've seen before include "Opposite of downs" , "Sup in good times" , "successes" , "Gains and losses - . . . and downs" , "Periods of good fortune" .)