A seventh part of labour production in month — increased by permit (9)
I believe the answer is:
septuplet
'a seventh part of labour production' is the definition.
I can't tell whether this definition defines the answer.
'month increased by permit' is the wordplay.
'month' becomes 'sept' (Sept is an example).
'increased' becomes 'up' (something that's up has increased or risen).
'by' means one lot of letters go next to another.
'permit' becomes 'let' (synonyms).
'sept'+'up'+'let'='SEPTUPLET'
'in' is the link.
Can you help me to learn more?
(Other definitions for septuplet that I've seen before include "Quick notes" , "One in large family" , "unusual baby" .)