Hat put back on after conclusion of matins (7)
I believe the answer is:
stetson
'hat' is the definition.
(Stetson is an example)
'put back on after conclusion of matins' is the wordplay.
'put back' becomes 'stet' (I've seen this in other clues).
'after' says to put letters next to each other.
'conclusion of' says to take the final letters.
The final letter of 'matins' is 's'.
'on' after 's' is 'son'.
'stet'+'son'='STETSON'
(Other definitions for stetson that I've seen before include "Hat with broad brim and high crown" , "Tip" , "Hat with wide brim and high crown, maybe a cowboy's" , "Capital investment" , "Hat for country-and-western singers, Texan oil magnates, etc." .)