I'll get in touch with you three hours after I'm finished running my errands.
I'll call you in about three hours after I take care of my business.
ーI'll get in touch with you three hours after I'm finished running my errands.
「用事を終えた3時間後に連絡をします」
to get in touch with ... で「…に連絡する」
to run one's errands で「用事を済ませる」
ーI'll call you in about three hours after I take care of my business.
「用事を済ませた3時間後に電話するね」
in about three hours after ... で「…の後3時間後くらい」
to take care of one's business で「用事を済ませる・用事を片付ける」
ご参考まで!