Apple was a co-founder of ARM Holdings (along side Acorn and VLSI Tech). I don't know how much stock they hold now, but Wikipedia says they held almost 15% in 1999.
In the 2010-ish time, there was a huge mystery corporation looking into buying MIPS before it was ripped into pieces (with the actual MIPS design team going to Imagination Technologies). It's worth considering that ARMv8 64-bit is extremely similar to the MIPS ISA.
Insiders have expressed surprise at Apple's progress. It takes 4-5 years to make and launch a new architecture (and A7 was completely new in every aspect). The starting mark for a third-party design should be from Oct 2011 when the ARMv8 ISA was announced. What's the actual time to a shipping product?
* Apple A7 -- (Sept 2013) 1 year 11 Months
* A53 -- (mid 2014) 2.5 years
* Apple A8 -- (Sept 2014) 3 years
* A57 -- (Q1 2015) 3.5 years
* Apple A9 -- (Sept 2015) 4 years
* Kryo -- (Dec 2015) 4 years 3 months
* A72 -- (Q1 2016) 4.5 years -- basically a fixed A57
How did Apple design such a fast chip in less than 2 years? They did not. Even Intel with a virtually unlimited budget, many more designers, and in-house fabs can't make that happen (PA Semi was good, but not that good). Apple had to know about the new ISA when apparently no other companies did. If ARM told only Apple about the upcoming ISA, that could easily run afoul of regulators.
Here's what I speculate happened. ARMv7 is holding back chip design. Apple looks into buying MIPS because its a great ISA, but changing architectures without backward compatibility is super risky (this was during the app war period). You don't do risky if you don't have to.
Start designing a chip using a new ISA that's very similar to MIPS (a known good starting point to reduce design time). Approach ARM with the options. You can turn that ISA into a new MIPS ISA pretty easily or you can hand over that ISA for ARM to release with guaranteed backward compatibility. Between the long-time business connections, fear of losing Apple, and the fact that it's a good design, ARM agrees. MIPS is divided up with ARM buying rights to most of their patents (basically eliminating the chances of ARM getting sued over ISA similarities).
ARM starts on their own designs and releases the ISA 6-10 months later. Apple chips launch when expected (and have a multi-year lead). ARM chips launch when expected given a few months insider info. Kryo and other third-party cores launch when expected compared to the ISA release.