Doctors, engineers and soldiers run into sailors (10)

'doctors engineers' is the definition.
'registrars' can be an answer for 'doctors'. I'm unsure of the 'engineers' bit.

'soldiers run into sailors' is the wordplay.
'soldiers' becomes 'regis' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'run' becomes 'r' (cricket abbreviation).
'into' is an insertion indicator.
'sailors' becomes 'tars' (tar is a kind of sailor).
'r' going into 'tars' is 'trars'.
'regis'+'trars'='REGISTRARS'

'and' is the link.