The traditional British (RP) pronunciation of clandestine stresses the second syllable, and reduces the third vowel to the short '-i-' of 'it', 'in' etc - 'clan-DEST-in', IPA: /klæn 'dɛs tɪn/. This is the pronunciation likely to be favoured by teachers, particularly those of a certain age.
The adjective clandestine means 'secret'. 'private' - usually with connotations of 'furtive', 'underhand' - and is typically applied to unethical, immoral or criminal behaviour. At times, it is used to describe matters related to espionage - not necessarily pejoratively when the spies are working on the same side as the writer.