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I wonder in this case if there is any rule that turns H to P.
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pronunciation
Why is 輩 in 先輩 pronounced ぱい while 輩 in 後輩 is pronounced はい?
Why? Well, it was practically for the same reason that English-speakers
"stopped" pronouncing the "gh" in words such as "night", "daughter", etc. many
years ago. The "gh" part was simply too difficult to keep pronouncing.

Likewise, it was and still is a little bit difficult for native Japanese-
speakers to say out loud 「せん **は** い」, so we started pronouncing it as 「せん
**ぱ** い」.

Not that you would need to remember this big technical term if you are a
beginner, but this phenomenon is called 「半濁音化{はんだくおんか}」. My own translation of
that would be " ** _P-sound-ification_** ".

**半濁音化 mostly occurs in Sino-loanwords used in Japanese. The H sound turns
into the P sound when it follows, for the most part, a 「ん」 or 「っ」 (small っ)**.

先輩 (one's seniors): せん **は** い ⇒ せん **ぱ** い

審判 (umpire): しん **は** ん ⇒ しん **ぱ** ん

絶品 (object of superb quality): ぜっ **ひ** ん ⇒ ぜっ **ぴ** ん

脱皮 (molting): だっ **ひ** ⇒ だっ **ぴ**

The list will be almost endless as we use tens of thousands of Sino-loanwords.
Unlike what some Japanese-learners mistakenly seem to believe, the **_vast_**
majority of our loanwords come from Chinese and certainly not English.
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answer
**TL;DR**  
In Japanese (native) and Sino-Japanese words, ん and っ make the next consonant
//h// to //p//. The sound change is a grammatical demand that no longer has
phonetic ground, as much as English _criti **c**_ vs _criti **c** ize_.

* * *

**Long story**  
Once upon a time, the Japanese consonant that we today call //h// had the
sound [[p]]. This sound was weakened to [[ɸ]] by at latest 10th c.
([母は昔はパパだった](http://www.iciea.jp/i-news/pdf/107/i-News107-15.pdf)), then to
[[h]]-like sounds (except ふ) by at latest 18th c.
([ハマの二つは唇の軽重](http://ijustat.com/nihongo/uirou.html)). But there are two cases
that these changes were met with resistance.

  1. //p// preceded by consonantal element, now converged into either ん (nasal stop) or っ (reduplication)

> 歩 [[po]] → [[ho]] "step" : 一歩 [[it.po]] → [[ippo]] "one step"  
>  歯 [[pa]] → [[ha]] : 出歯 [[de.ba]] "bucktoothed"
> ([rendaku](https://en.wikipedia.org/wiki/Rendaku)) : 出っ歯 [[deʔ.pa]] →
> [[deppa]] "bucktoothed (slangy)"  
>  輩 [[pai]] → [[hai]] "fellow" : 先輩 [[sen.pai]] → [[sempai]] "senior"

  2. mimetic words; that carry sound symbolism unlike usual words

> ぴかぴか [[pikapika]] < 光 [[pikaɾi]] → [[çikaɾi]] "light"  
>  ぱたぱた [[patapata]] < はたく [[pataku]] → [[hatakɯ]] "pat, rap"

From today's perspective, it seems that //h// occasionally turns into //p//,
but it's actually //p// is occasionally retained until today.

**PS**  
ヨーロッパ, the Japanese transcription of Portuguese
[_Europa_](https://en.wiktionary.org/wiki/Europa#Portuguese), attests two
important facts at the Late Middle Japanese stage: (1) reduction of diphthongs
//eu// → //joo//; (2) //p// unable to appear in the middle of word without
reduplication *//-pa// → //-Qpa//.
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