Pull bat away regularly after proper bloomer (7)
I believe the answer is:
primula
'bloomer' is the definition.
(type of flower, something which blooms)
'pull bat away regularly after proper' is the wordplay.
'away regularly' indicates alternate letters (letters taken away at regular intervals).
'after' says to put letters next to each other.
'proper' becomes 'prim' (similar in meaning).
'pull'+'bat'='pullbat'
The alternate letters of 'pullbat' are 'ula'.
'ula' put after 'prim' is 'PRIMULA'.
(Other definitions for primula that I've seen before include "Cowslip genus" , "Plant such as cowslip" , "Cowslip relative" , "Primrose" , "Polyanthus" .)