Problem with glasnost, oddly, recalled (4)
I believe the answer is:
snag
'problem' is the definition.
(thesaurus)
'glasnost oddly recalled' is the wordplay.
'oddly' means one should take alternating letters.
'recalled' is a reversal indicator.
The alternating letters of 'glasnost' are 'gans'.
'gans' reversed gives 'SNAG'.
'with' acts as a link.
(Other definitions for snag that I've seen before include "Difficulty; catch" , "Hidden obstacle or drawback" , "A hidden or unexpected obstacle" , "Minor hitch" , "Catch - disadvantage" .)