Variable administrators of chess taking step back to improve (5)
I believe the answer is:
edify
'improve' is the definition.
(thesaurus)
'variable administrators of chess taking step back' is the wordplay.
'variable' becomes 'y' (I've seen this in other clues).
'administrators of chess' becomes 'fide' (international chess federation FIDE).
'taking step back' is a reversal indicator.
'y'+'fide'='yfide'
'yfide' reversed gives 'EDIFY'.
'to' is the link.
(Other definitions for edify that I've seen before include "improve mentally" , "Change for the better" , "Improve understanding" , "Educate, uplift" , "Tutor" .)