Minutes are a record of decision with minimal additional information other than to give context to the decision. In this scenario, if I've understood it properly, the HR committee would discuss the proposal and resolve to recommend to full council that the subscription be paid (assuming of course that was what was agreed). At full council, there would be a recommendation from the HR committee to recommend payment with a decision taken. Whilst full council can question the recommendation, I would not have expected the recommended course of action to be discussed in detail - that is what the committee meeting is for - but if discussion started to stray into personal or confidential areas, a motion to move into confidential session could be proposed as it is one of the proposals that can be moved without prior notice.
It is not the clerk's role to make decisions about the terms of reference of any committee as that is the job of the council and if that committee has no authority to approve payments, that authority cannot be delegated on the whim of the clerk or indeed anyone. Similarly, the minutes should reflect the decision taken by both bodies and nothing else unless absolutely necessary.