No trigger needed!!
Just use an INSERT command. The thing you need to take care of is that the value of "users_id" you enter in the [travel_request] table must allready exists in table [users]. The code below give you two possible solutions. The first will insert all values hard-coded. The second will insert the values and searches the "users_id" that belongs to the given "username".
-- insert values hard-coded
insert into travel_request values(1, 3, 200, 'me')
-- insert values and search the "users_id" from the [users] table
insert into travel_request
select 2, users_id, 500, 'me'
from users
where username = 'Ram'
select * from travel_request