Bearing first of children with Mike out of wedlock (8)
I believe the answer is:
carriage
'bearing first' is the definition.
'carriage' can be an answer for 'bearing' (I've seen this before). I'm not sure about the 'first' bit.
'children with mike out of wedlock' is the wordplay.
'children with' becomes 'c' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'mike' becomes 'm' (phonetic alphabet: alpha, bravo, charlie etc.).
'out of' is a deletion indicator.
'wedlock' becomes 'marriage' ('marriage' can be a synonym of 'wedlock').
'marriage' with 'm' removed is 'arriage'.
'c'+'arriage'='CARRIAGE'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for carriage that I've seen before include "Posture; conveyance" , "Conveyance, its cost" , "Railway vehicle" , "Bearing - conveyance" , "Bodily posture or wheeled vehicle" .)