How to insert values into two tables with a foreign key relationship?

Use SCOPE_IDENTITY() second insert into tblRoleOfStuff on a place of StaffId. Like:

insert into tblStaff values
(@name, @age, @address)

insert into tblRoleOfStuff values
(scope_identity(), @roleid)

EDIT

There too much comments on this answer, so I want to give an explanation.

If OP guarantee that he will not use any triggers he may use @@IDENTITY (bad practice), it is sufficient enough to his needs, but best practice to use SCOPE_IDENTITY().

SCOPE_IDENTITY(), like @@IDENTITY, will return the last identity value created in the current session, but it will also limit it to your current scope as well. In other words, it will return the last identity value that you explicitly created, rather than any identity that was created by a trigger or a user defined function.

SCOPE_IDENTITY() will guarantee that you get identity from current operation, not from another connection or last one processed.

Why not IDENT_CURRENT? Because

IDENT_CURRENT is not limited by scope and session; it is limited to a specified table. IDENT_CURRENT returns the identity value generated for a specific table in any session and any scope.

So you make take last scoped but not current one. Yes, OP can use it too, but it is a bad practice in that situation (like using only @@IDENTITY)

Using OUTPUT is indeed good practice, but over complicated for only one identity. If OP need to process more then one row in a time - yes, he need OUTPUT.

You can use output from your first insert statement.

declare @tmp table(id int)
insert tblStaff (name, age, address)
OUTPUT inserted.Id INTO @tmp (id)
values (@name, @age, @address)

declare @roleId int = 1 --or whatever
insert tblRoleOfStaff (staffId,roleId)
select id, @roleId
from @tmp

You can insert several roles at once as well.

create table Roles (roleId int identity(1,1) primary key, 
RoleName varchar(50),
isDefaultRole bit default 0
)
--mark some roles as default (`isDefaultRole = 1`)
--the 2nd insert will be
insert tblRoleOfStaff (staffId,roleId)
select id, roleId
from @tmp
cross join Roles
where isDefaultRole = 1

Because it seems like you are discussing 1 row at a time some people may tell you to use a system vairable like @@IDENTITY or some of the others but to ensure with more certainty I recommend the OUTPUT clause of the insert statement. The good thing about this method is it can easily be adapted to handle more than 1 row at a time.

DECLARE @Output AS TABLE (StaffId INT)

INSERT INTO tblStaff (name, age, address)
OUTPUT inserted.Id INTO @Output (StaffId)
VALUES (@name, @age, @address)

DECLARE @StaffId INT
SELECT @StaffId = StaffId FROM @Output

INSERT INTO tblRoleOfStaff (StaffId, RoleId)
VALUES (@StaffId,@RoleId)

Reasons not to use @@IDENTITY in case another operation linked to yours is performed. E.g. a trigger inserts another row into another table, or updates another record in your database., SCOPE_IDENTITY has a similar shortfall when a trigger modifies the same table. IDENT_CURRENT has a short coming too. Do an internet search to learn more there are tons of great resources on these.