Exercise too much in public, then shower? (9)
I believe the answer is:
overtrain
'exercise too much' is the definition.
'public then shower?' is the wordplay.
'public' becomes 'overt' ('overt' is associated in meaning with 'public').
'then' means one lot of letters go next to another.
'shower?' becomes 'rain' (shower is a kind of rain).
'overt'+'rain'='OVERTRAIN'
'in' is the link.
(Other definitions for overtrain that I've seen before include "Run past peak, perhaps" , "Spend too much time on exercises" , "Prepare too hard" .)