Execution plans behavior after a restart in SQL server
This is what happens when you restart SQL Server. Correct term will SQL Server has to create new execution plans, choose the 'reasonably good one' and save it in the cache to reuse.


  or instead, SQL will need to create new execution plans library in
  order to keep on improving the executions?


You have some misconception about execution plans in your question.

Plans are not updated after each execution. SQL Server keep tracks of how many time a plan was used, last used, and few other metrics. If you have memory pressure the usage metrics is used to decide which plans need to be removed to free up memory.


  Actually, after each execution, those plans are updated to let the SQL
  learn itself about new improvements.


You can manually remove plans from cache, details here.

There are improvements announced for SQL vnext (2017) to adjust/modify query plan on the fly called Adaptive Query Processing . You can watch a video by Microsoft Product Manager Joe Sack.here and read here.