Memorable year, after slight problem (6)
I believe the answer is:
catchy
'memorable' is the definition.
(something catchy is easy to remember)
'year after slight problem' is the wordplay.
'year' becomes 'y'.
'after' says to put letters next to each other.
'slight problem' becomes 'catch' (what's the catch?).
'y' put after 'catch' is 'CATCHY'.
(Other definitions for catchy that I've seen before include "Of tune, lilting and easy to remember" , "Readily caught, like a tune" , "Type of tune that stays in the memory" , "Of a tune, lively and easy to remember" , "Hummable" .)