unengaged
1. [ adjective ] not busy or occupied; free
Examples:

"the cancellation left her unengaged a good part of the afternoon"

Related terms: idle
2. [ adjective ] not promised in marriage
Synonyms: unpromised unpledged
Examples:

"continued seeing him but on an unengaged basis"

Related terms: unattached
Similar spelling:   unhinged
  unmingled
  unhinge
  uninsured
  uninjured