Most Presbyterians know that a Clerk of Session must be an elder. It's not so well-known that the Clerk of Session need not be a currently-serving member of Session.
Form of Government G-9.0203b says: "The clerk of the session shall be an elder elected by the session for such term as it may determine." It says nothing about having to be a current Session member - which is quite intentional. The language is permissive, either way.
A Clerk who is serving a term on Session concurrently with serving as Clerk is entitled to join in debate and vote on motions brought before the Session. A Clerk who is not an elected Session member is not entitled to vote, and should refrain from joining in debate - although most Sessions offer their Clerk the privilege of the floor in order to address matters related to the smooth handling of Session business.
It's common practice, in many of our churches, for Clerks to be elected on an annual basis, along with other corporate officers such as the Treasurer and the President of the Board of Trustees. Generally, in "unicameral" congregations (where the Session members are also the Trustees), the Clerk of Session is also the Secretary of the Corporation.
Unlike members of Session (who, according to G-14.0222, can only be re-elected once, after which they have to sit an election out before returning), the Clerk of Session may be re-elected any number of times in succession. Many churches in Monmouth Presbytery are fortunate enough to have Clerks who have served for quite a number of years. Long tenure in the Clerk's position is generally a good thing, because knowledge of the church membership and of the responsibilities of the office is a real plus. (As any new Clerk will tell you, there's quite a learning curve associated with stepping into the job for the first time, so it's good to be able to stick around for a while!)
Most pastors will be quick to affirm that a seasoned, experienced and supportive Clerk of Session is one of the greatest assets to their ministry, freeing them from minor administrative details so they can focus on caring for the flock.
So, we've established that the Clerk of Session doesn't have to be a currently-serving Session member. But, is it a good thing? Ultimately, that decision is up to the Session. Sessions that look outside their own membership to find an elder to serve as Clerk often do so because (1) it broadens the range of people they can consider, enabling them to find an elder with just the right skills, and (2) it frees up another seat at the Session table. (Most Clerks have their hands full with their clerkly duties and probably couldn't chair a committee or work group anyway.) Some Session members, upon being elected as Clerk, have actually resigned their position on Session, so as to enable someone else to come on board to fill their unexpired term.