Very neat in retrospect after biro's beginning to dry out (5,2)
I believe the answer is:
sober up
'dry out' is the definition.
'very neat in retrospect after biro's beginning' is the wordplay.
'very' becomes 'so' (I've seen this in other clues).
'neat' becomes 'pure' (both can mean undiluted).
'in retrospect' says the letters should be written backwards.
'after' says to put letters next to each other.
'beginning' indicates taking the first letters.
The initial letter of 'biro' is 'b'.
'pure' in reverse letter order is 'erup'.
'erup' put after 'b' is 'berup'.
'so'+'berup'='SOBER UP'
'to' is the link.
(Other definitions for sober up that I've seen before include "Become less drunk" , "Get real" , "What you do when drink wears off" , "become serious" .)