Why is 輩 in 先輩 pronounced ぱい while 輩 in 後輩 is pronounced はい?

Question

I wonder in this case if there is any rule that turns H to P.

Answer 1

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 critic vs criticize.

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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), then to [[h]]-like sounds (except ふ) by at latest 18th c. (ハマの二つは唇の軽重). 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) : 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, 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//.

Answer 2

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.