engaged
adjective
uk/ɪnˈɡeɪdʒd/ us COMMUNICATIONS UK
if a telephone is engaged, someone is already using it:
Customers calling to book tickets found the line was constantly engaged.
See also
busy
busy doing something:
The president is currently engaged but you can meet with his deputy.
be engaged as sth
to be working as something:
At that time she was engaged as an adviser to several government departments.
be engaged in sth
to be involved in something:
The broadcaster is engaged in a complex legal battle over a failed joint venture.