With Prime Minister at first is causing trouble (8)
I believe the answer is:
mischief
'trouble' is the definition.
(I've seen this before)
'with prime minister at first is' is the wordplay.
'with prime minister' becomes 'm' (I can't justify this - if you can you should give a lot more credence to this answer).
'at' is a charade indicator (letters next to each other).
'first' becomes 'chief'.
'chief' after 'is' is 'ischief'.
'm'+'ischief'='MISCHIEF'
'causing' is the link.
Can you help me to learn more?
(Other definitions for mischief that I've seen before include "Playful troublemaking" , "nuisance" , "Devilment, impishness" , "Black . . . . . . . . (Evelyn Waugh)" , "Naughtiness, devilment" .)