CLI is also a TLA for Calling Line Information, information on a phone call which tells the recipient your number. It is used by ISPs and is required to be sent to use the Caller ID feature of some phones and to use the 1471 number.
CLI can be temporarily witheld by dialling 141 before calling or it can be permamently witheld by phoning a special number maintained by BT.

Please note: To the best of my knowledge this only applies in the UK.

cf. 1471 and 141.