I've been searching all over the Internet for the answer and can't find anything so hoping someone can point me in right direction. The scenario is on 6th Sept our flight was delayed then eventually cancelled. We were given a replacement flight for following day. That flight ended up being delayed and landed 4 hours late. So my question is when applying for compensation do I apply for cancellation or delay or both? If both do I do two separate claims? One for the cancellation and one for the delay? They were 2 separate flight numbers but with same airline.

Travellingbird Welcome to FT
Note from your profile from GB.
Cannot double dip. If you are claiming as UK261, and not an extraordinary reason, compensation is based on your arrival time vs scheduled arrival time. What happens in between is irrelevant.
If you list details of your flight this thread will likely be moved to that airline subforum

Welcome to FT!

Could you please let us know the itinerary and the airline involved? The reason for asking is that it matters in respect to applicable regulation as EU Reg 261/04 only covers certain flights (FROM EU) and certain airlines TO the EU. Similar if this are UK flights where UK261 will apply. If you prefer not to disclose the itinerary could you at least let us know the destination and it the airline is EU or UK based?

In general, you can claim for comp. for cancellation of the first flight. If you were rebooked to a new flight you can claim for delay of this flight as well as it is two separate flights/events. If it is a true replacement flight, i.e. a new aircraft to performe the cancelled flight, it is not two events and you can only claim for delay (as the flight wasn't cancelled). In fact it is easier if you were rebooked to a different airline as then you could claim comp. for cancellation with airline A and for delay with airline B. From your post I assume it is the same airline but the info on how the "new" flight was organised (rebooked to different flight No.? - or only aircraft replacement?) is critical and missing from your post.

No doubt that the airline is going to resist to pay 2x comp. and will most likely try to weasel out of paying comp. twice. Also do note that if the cancellation or delay was caused by extraordinary circumstances/outside the control of the airline, you are not eligible for comp. and it will be denied by the airline.

Could very well be two separate claims, however providing more details will enable better answers to your questions.

Welcome to FT !

Threads like these are A LOT easier to evaluate when OPs provide even a slither of relevant information (e.g airline and origin/destination countries if you want to remain somewhat elusive; include date and flight number if you want a more useful assessment).

Even a sliver would do.