It sounds like he was pleased or entertained (amused), but uneasily (tense) so. Something made him nervous or anxious but also somehow entertained him at the same time.

Tense usually has a negative connotation to it but since it says that his eyes “glittered” with tense amusement I would assume that something caught his eye (got his attention in a positive way) and he’s fixated on it because he finds it interesting, attractive, and intriguing. 🌈 Nicky

I think you can remove "a" and just say tense amusement. Tense is not a word I would ever associate with amusement, but I suppose it would mean strong or intense.

"a" is unnecessary. You can just say "His eyes glittered with tense amusement." It means that his eyes glittered with amusement, that is you could see amusement in the look of his eyes. Furthermore, that amusement seemed to convey tension.