The president proposes a highway construction bill to congress and then pressures lawmakers to pass the proposed legislation. which role is the president fulfilling?

I believe the role is: chief legislature
As a chief legislature, we could argue that president has the highest power in determining which bill would be passed by the government.
On top of that, the president also had the right to veto any bills that proposed by Congress in order to keep the bill in the president's favor.

Sector is best defined as (part).