My deodar cedar drips a lot and an arborist told me the tree has ongoing pest problems. Could the tree have aphids?
There are several possible causes for the dripping of your Cedrus deodara. It might be honeydew (from an insect infestation). There is a type of aphid, Cinara curvipes, the bowlegged fir aphid, which feeds on cedar bark. Large colonies of aphids can develop on the twigs or branches of host trees in the winter along the Pacific Coast, or in the spring inland. Vast amounts of honeydew can rain down if the infestation is heavy. If you shake an infested branch, aphids should drop from it.
(Source: Insects that Feed on Trees and Shrubs by Warren T. Johnson and Howard H. Lyon, 1994)
If, in addition to the oozing sap, the foliage is also discoloring and wilting, it could be caused by a root or crown rot.
(Source: Pests of Landscape Trees and Shrubs, 2nd edition, by Steve Dreistadt, 2004)
Since there could be many causes, it might make sense for you to bring in a sample to a Master Gardener Clinic. You can locate a Master Gardener Clinic within King County on this website (Plant Clinic Schedule, or statewide here.