unengaged

adjective

1. busy or occupied; involved: deeply engaged in conversation.
2. pledged to be married; betrothed: an engaged couple.
3. under engagement; pledged: an engaged contractor.
4. entered into conflict with: desperately engaged armies.
5. Mechanics.
   1. interlocked.
   2. (of wheels) in gear with each other.
6. Architecture. (of a distinct member) built so as to be truly or seemingly attached in part to the structure before which it stands: an engaged column.

adjective

1. pledged to be married; betrothed
2. employed, occupied, or busy
3. architect built against or attached to a wall or similar structurean engaged column
4. (of a telephone line) already in use