A chairde,

Could anyone provide a translation of the Motto of the Clan Hannay
PER ARDUA AD ALTA (Through difficulties to higher things),

into Irish
and/or Scots Gaelic?

Go raibh míle maith agaibh,
Gearóid

Maybe Trí chruatan go nithe móra

That's a bit bit literal for my liking, though, the second part specifically. "higher things" is more subtle than "nithe móra".

Trí chruatan a sháraítear I think this would be an acceptable way of expressing "Through difficulties [does one] overcome"

Wait for more.

Perhaps simply:

Trí chruatan in airde

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Does that convey the higher things part, though?

I think ad alta just means "to high things" or even "to heights".

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Wouldn't go be better then? But then of course go hairdí (sp?) doesn't sound great

Why not "trí chruatan suas"?
(Ulster: fríd chruatan suas)

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

That approach would be pretty east to put into Scottish Gaelic:

Tro chruadalan suas [using a word for difficulty/adversity which is cognate with the Irish one, and perhaps easier to pronounce]
or
Tro dhuilgheadasan suas [using a more common word for difficulty]

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.

Go raibh maith agaibh.

Gearóid