Pebbledash repair

Hi peeps, looking for some advice. I have a small (very old) conservatory on the back of my house, the walls of which are externally covered by pebbledash. I have just noticed a narrow crack in the pebbledash where it appears to be lifting. I think it may be due to a gutter corner joint that came adrift a few months ago (already fixed) that let water get in behind the rendering. I think it’s a repair I can probably tackle myself but I want to know the best sort of render to use, type of shingle to make good and, also, a good external wall covering to help keep any dampness out going forward.
Thanks in anticipation. Keith

 

Looks like a white chip which has been painted.
Hack out the crack and see how deep it goes.