Agree not Ligustrum.
Nor Ilex.
Interesting.....
It sort of reminds me of a New Zealand plant I know.
I knew it as Hebe hulkeana but checking www I see it is now called Veronica hulkeana.
Maybe worth checking.
Evergreen/opposite leaves,/margins toothed/ pretty flowers in lax panicles or raceme.
https://www.nzplants.auckland....
