Close to centre, from memory (2,5)
I believe the answer is:
by heart
'from memory' is the definition.
(I've seen this before)
'close to centre' is the wordplay.
'close' becomes 'by' (I've seen this in other clues).
'to centre' becomes 'heart' ('heart' can be a synonym of 'centre').
'by'+'heart'='BY HEART'
(Other definitions for by heart that I've seen before include "(Learnt) in memory" , "One way to remember" , "To know - - is to have in the memory" , "Off pat" , "Parrot-fashion" .)