Period caught in New York office (6)
I believe the answer is:
agency
'office' is the definition.
(I know that office can be written as agency)
'period caught in new york' is the wordplay.
'period' becomes 'age' (age is a kind of period).
'caught' becomes 'c' (cricket abbreviation).
'in' indicates putting letters inside.
'new york' becomes 'ny'.
'c' put inside 'ny' is 'ncy'.
'age'+'ncy'='AGENCY'
(Other definitions for agency that I've seen before include "Business organisation" , "Government office" , "Bureau; instrumentality" , "Organisation providing a particular service" , "Recruitment bureau" .)