Frenchman has new tree to measure (5)
I believe the answer is:
meter
'to measure' is the definition.
(I know this)
'frenchman has new tree' is the wordplay.
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'has' means one lot of letters go next to another.
'new' indicates an anagram.
'tree' with letters rearranged gives 'eter'.
'm'+'eter'='METER'
(Other definitions for meter that I've seen before include "Poe sometimes used this" , "Device that measures, say, electricity usage" , "Something measuring" , "Device for recording, say, usage (5)" , "Measuring device as for electricity usage (5)" .)