The subject of what military an independent Scotland might have has gathered a lot of attention. One of the most serious and definitive reports on the matter comes from the respected Royal United Services Institute, a piece entitled “A’ the Blue Bonnets.“
The RUSI piece in short depicts a small and light land force not too dissimilar from Ireland’s, unsurprising in light of their similar geography. However it does assume a more capable air/naval element. The report shows a comparably strong navy and an air force with hand-me-down BAE Hawks as its fixed-wing fighters.
Assuming no political issues, something like the KAI Golden Eagle might also work as a basic air defense fighter, an heir to the F-5 of the past. That’s the only real quibble I have with the report, which is otherwise well worth a read.
As for the possible opponents of this Scottish military, far and away the most realistic is, like Ireland, whoever they’d face on foreign peacekeeping operations. For more out-there ones, you have Russia (especially at sea), and if you want to be really out there, you could do a “Kobayashi Maru” situation where the Scots have to inflict as much damage on the invading English/British invaders as possible.
And of course, this assumes a commitment to plausibility-if you strip-mined Scotland’s entire military age population and had an outsider equip and train it, then you could end up with something completely gigantic. But the “Ireland on land and another North Sea state on sea and air” option is the most logical.