So i was given this iten by the jarl in solitude. She told me to place it at the shrine of talos but I have no quest for it and can't get it out of my inventory. Any ideas on what to do?

Check that you've tagged Miscellaneous quests in the start menu.

Yeah it's a misc quest, otherwise if it's still not there...

Alright I'll try that

It is interesting that the sort of defacto Leader of the Jarls, supposedly held to the White gold Concordat, would send you to make the offering to the forbidden God Talos.

Makes me think how much strife sits under the surface ready for a well places and paced DLC.

It's like the blacksmith in Riverwood says at the start of the game. The White Gold Concordant really didn't mean much. Officially, Talos was stricken from the Divines, but he was still privately worshiped by the people. The Empire's official stance was "That's illegal," but they didn't seem to be that concerned with it. That is of course until Ulfric and the Markarth Incident got the attention of the Thalmor.

The Jarl of Whiterun also secretly worships Talos (as his son tells us). My bet is that if there is a DLC surrounding the election of a new high king at a Moot, he would be the canon choice. Satisfies both sides since he sides with the Imperials but still worships Talos.