Aiming to have member accepted by Old King's school (8,7)

'school' is the definition.
(training college is a kind of school)

'aiming to have member accepted by old king's' is the subsidiary indication.
'aiming' becomes 'training' ('train' can be a synonym of 'aim'**).
'to have' says to put letters next to each other.
'member' becomes 'leg' (leg is a kind of member).
'accepted by' means one lot of letters goes inside another.
'old king' becomes 'cole'.
'leg' inserted inside 'cole' is 'college'.
'training'+'college'='trainingcollege'