It would seem that all the commas in your text were removed:

Without prejudice to the generality of the provisions of the foregoing clause A.ll.l, and
subject thereto, the Trustees, in exercising any of the powers vested in them in favour of
any particular person, may ignore entirely the interests of any other person interested or
who may become interested under this trust, and in particular (but without prejudice to the
generality of the foregoing) no APPOINTMENT, ADVANCEMENT, OR APPLICATION made in exercise of any power shall be invalid on the grounds that:
A.ll.2.1 an insubstantial, illusory, or nominal share is appointed, or advanced to, or applied
for any objects of such power, or left unappointed, unadvanced, or unapplied; or
A.ll.2.2 any objects of such power are thereby altogether excluded;

So here, we are talking about the way the trusts assets may be allocated to different persons.
"Appointment" refers to the "power of appointment", i.e. the power to decide on the disposal of property, i.e., who gets what from the trust (it's not about "appointing someone" in the sense of appointing them to a position, so I wouldn't translate it as "nombramiento" or "designación", unless you want to explain it further by saying "poder de nombrar/designar herederos de bienes"). In Spanish, this is usually known as "adjucación de bienes o efectos":

"A power of appointment is a power to determine who will receive property. Essentially, the settlor is (sort of) "delegating" to someone else, the future decision on who gets some property."
...
As you can see they work like a power of attorney. The power holder decides where and when the property will be transferred but the transfer (conveyance) actually comes from the property holder.
http://wynnwilliams.bp-dev.co.nz/getattachment/28f7700d-62bf...

From the above, it is clear that this sense of "appointment" is the power to decide "who gets what". "Appointment" in this sense is even broader than "distributing the estate," as it also involves deciding on

"Advancement" is a related term, in that it refers to the power to transfer property to a beneficiary early.

"A power of advancement is a power to transfer property to a "final" beneficiary (say a child entitled to receive an inheritance on reaching 25) early. It is different to a power of appointment in a number of ways but essentially under a power of advancement the beneficiary is already entitled to the property they just get it early."
http://wynnwilliams.bp-dev.co.nz/getattachment/28f7700d-62bf...

I believe "application" here is meant in the sense of using a property to make a payment to, or for the benefit of, beneficiaries (i.e., "aplicar" or "destinar"), according to sense (2) of the Black's Law (8th Ed., p. 310) definition:

"APPLY"
2. To employ for a limited purpose <apply payments to a reduction in interest>"

On "appointment", there are many entries in the glossary, but most seem to favour "designación" or "nombramiento," although, in my opinion, because of a lack of understanding of the term (understandably confusing it with the power to appoint people to positions).

Here is an earlier KudoZ question (the correct answer by "KirstyMac", poder general de adjudicación de bienes fideicomisados [sic], was not chosen, unfortunately).
https://www.proz.com/kudoz/english-to-spanish/law-general/73...

I would translate it as "...ningún acto de adjudicar, adelantar o destinar bienes que se realice en ejercicio de cualquier poder..."