Picks clubs and hearts, having zero diamonds and spades (7)
I believe the answer is:
choices
'picks' is the definition.
('choice' can be a synonym of 'pick')
'having zero diamonds and spades' is the wordplay.
'having' becomes 'ch' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'zero' becomes 'o'.
'diamonds' becomes 'ice' (I've seen this before).
'and' is a charade indicator (letters next to each other).
'spades' becomes 's' (abbreviation in card games).
'ch'+'o'+'ice'+'s'='CHOICES'
'clubs and hearts' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
(Other definitions for choices that I've seen before include "Options, alternatives 97)" , "Selections" .)