It is probably very uncommon to serve for years and years in the same position. For most, you get an assignment, and work there for 3 months, 6 months, maybe a year or two. Deep space missions create a different climate, but when you get back, you get a promotion.
The Enterprise was a new ship, a flagship, and was not on long deep space missions. A lot of its early assignment were pomp and diplomacy, and many episodes both began and ended at a starbase.
For the first year, chief engineers came and went. Most probably had 3 month assignments, where they would have the option of continuing if the Captain so chose. Most likely served for 3 months, were offered a plum position or promotion elsewhere, and moved on. Eventually, both starfleet and Picard felt the need for a more stable element, reorg, etc. LeForge was promoted, and worked out so well that he stayed right where he was, to everyone's satisfaction.