Party up with detectives ... for a price (4)
I believe the answer is:
odds
'price' is the definition.
(I've seen this before)
'party up with detectives' is the wordplay.
'party' becomes 'do' (do can informally mean a party).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'with' is a charade indicator (letters next to each other).
'detectives' becomes 'ds' (I can't justify this - if you can you should believe this answer much more).
'do' back-to-front is 'od'.
'od'+'ds'='ODDS'
'for a' is the link.
Can you help me to learn more?
(Other definitions for odds that I've seen before include "Scraps" , "Chance" , "Betting rates" , "Indicator of likely betting winnings" , "Chances, probability" .)