Hire a new gang in extremes of exigence (6)
I believe the answer is:
Here is my best explanation:
'hire' is the definition.
'a new gang in extremes of exigence' is the wordplay.
'a new' indicates anagramming the letters.
'in' means one lot of letters goes inside another.
'extremes of' says to hollow out the word (remove centre letters).
'exigence' with its middle removed is 'ee'.
'gang' with letters rearranged gives 'ngag'.
'ngag' put inside 'ee' is 'ENGAGE'.