Sent to the hold and cleared for approach before reaching holding fix

Someone would need to ‘code’ buffers into the segments of either time or distance if the ‘box is to make a decision that ’well we’re here so we’ll continue to do this’. Some of that does exist such as when the box sees an acute turn angle and turns miles early.
In this scenario I feel it’s important to take command and decide.
That may agree or disagree with the box.
In this case of armchair diagnosis, I’d overfly the fix and teardrop backto it .
However I have to admit, in flight there’s a high chance that above MSA I’d directly react to ATC and immediately commit to a turn before thinking the best option is to make the procedure turn.
Where it gets messy is that delaying the process messes with ATC’s situational awareness.
Possibly a problem they cause for themselves, where waiting 30 more seconds for you to reach the fix removes the ambiguity a bit. You landed so all is good.

Peter wrote:

So while I was under instruction to take up the hold, this was rescinded before reaching the holding fix.

I’m pretty sure this would have been my interpretation based on your description of the exchange. It seems no different than being cleared direct X waypoint, followed by a clearance a few minutes later direct Y waypoint. Unless the instruction is “after X, then direct Y”, the assumption is that X is now history. You were asked to hold, then you were cleared for the ILS via an alternate IAF. Having said that, I always ask before making any changes if it feels ambiguous.

I think the left turn would have been correct:

• “Cleared for ___ approach via X” implies “direct to X”, so the procedure turns via the hold are irrelevant here.
• For the RNP approach you aren’t supposed to turn more than 110 degrees at IAF
• This is not an RNP approach, but a kind of RNP initial approach for an ILS, so I’d expect the same rule as above.
• Of course you should not descend below the relevant MSA before reaching IAF (but it is 2000ft anyway).

Assuming you’re on with Lille at this point, given the MSA is 2000 and you’re 5 descending 3 then I’d be lazy and turn left as you don’t need terrain protection from the hold plus on with Lille I’m guessing you’re on a traffic service which means you have separation, then crossing Olmav at 3 cleared ILS the only thing I always verify is cleared to descend with the procedure but that’s the implication here anyway.

I did a ton of IR training at LFAT with SIMON Coombs and found it really great Lille always super helpful.

Being so close to/at OKPEM, the controller thought the same so I would cross OKPEM do the parallel entry to reach OKPEM again and head to OLMAV while descending to 2000 ft. If they want you to go directly somewhere, you will hear it. Now, being in a busy environment, that would be unlikely.

I checked on the GTN simulator and it seems to mostly agree. So depending on when given the clearance for the approach via OLMAV (in some examples I used high GS for an artificially high turn radius for better illustration) :

A) Before being abeam OLMAV inbound OKPEM

B) Abeam OLMAV inbound OKPEM

C) Past OLMAV inbound OKPEM

D) Entering the parallel hold at OKPEM

E) In the hold teardrop

F) In the hold turning outbound

G) In the hold outbound

H) Changing your mind a couple of times in a row

Peter wrote:

How about EGKA DCT OKPEM and then just before OKPEM cleared for the ILS (whatever that means to the GTN) via OLMAV.

That would be option C above, so a LH turn. GTN only changes to RH turn to OLMAV if selected after initiating the RH turn for the parallel entry.