I agree with ratter, leylandii will not shoot fresh growth from old wood.
My guess is its an old hedge thats become overgrown for your needs or a young hedge that may have suffered drought.
Generally you can get away with trimming just once a year with leylandii but trimming more reularly, twice or even three times can keep a young hedge dence and compact and less trimmings to dispose of, but remember dont cut back too far. Good Luck. Tbird+
we let our hedge grow 4 20 years without any trimming and started cutting it back about 6 years ago, in stages there now down at 4m tall and still a little thin on the ground but, as a word of warning dont let them thin at bottom 2much before lopping the top which encorages side growth. but we have seen old wood produce new shoots only 2cm long and dont grow much after, but was always under the impression it never happend, not much use tho.