It seems like (thanks to the answerer below) the product contains potentially one haram ingredient namely rennet. It is extracted from the stomach of animals.
Traditional animal rennet is an enzyme derived from the stomachs of calves, lambs or goats before they consume anything but milk. Vegetable rennet is obtained from a type of mold (Mucur Miehei). However, even though it is derived from mold, there is no mold contained in the final product. It is an equivalent chymosin product which works equally well but is not animal derived.
I've skimmed the following articles for something haram based on the ingredients shown on the image, it seems you're not good to go. The only thing I'm concerned with is that it also shows the use of European and non-european products but it isn't specified. Inshallah there will be nothing haram in it.
So, I'd say enjoy your new vegetarian pesto. ;)
Apologies for the mistake.
If you want to get more info about the etiquette of eating in islam, feel free to go to the link below.