It has nothing to do with the individual firearm holder or their certificate. The "estate rifle" clause is written in to legislation. Anyone 17 years old or older (if the borrower is 17, the lender must be 18 or older) can borrow, and use, any section 1 weapon held on an FAC, under the supervision of the FAC holder.
The relevant legislation is here:-
Firearms (Amendment) Act 1988
There is much discussion about who can avail themselves of the clause.
"Occupier or servant of the occupier" is the first point of contention. The thinking seems to be that someone who holds shooting rights on the land (in writing to be safe) can rightfully claim to be an occupier.
"Servant of the occupier" is usually taken to mean one who is in "the normal employ" of the occupier, such as a gamekeeper or other employee.
Note that 1.B states that the firearm is used according to the conditions on the holders FAC.
The conditions states that the borrowing must take place "in the presence of" the FAC holder for the relevant rifle. "In the presence of" is usually taken to mean "in sight and earshot", although I'm not aware of any legal precedent on this.
So yes, it CAN apply to any weapon held on a S1 FAC (there is no such allowance for S5 weapons, or S2 either. You can lend someone a 30-06, but not a S2 12 bore. You can however lend a high capacity (S1) 12 bore!)
There is no such thing as an "estate clause" on a FAC. It is not something that can be "applied for".
I hope that kind of clarifies it.
BASC have a useful fact sheet on it.
https://www.basc.org.uk/download.cfm/docid/DB12FC55-AA2C-4E12-B87529F5D17C4E2F