Houston has no zoning, but that does not mean anything goes in the Heights. Two separate layers of rules can apply.
City historic districts. The City has designated three: Houston Heights Historic District East, West and South. Inside them, most exterior changes, additions, new construction, relocations and demolitions need a Certificate of Appropriateness from the City before work starts. Ordinary maintenance, in-kind repairs, landscaping and fences are exempt. The districts also have measurable standards. For example, side setbacks for additions and new construction are at least five feet on each side, with a combined 10 feet for one-story houses and 15 feet for two-story houses. Not every Heights address is in a district, so check the City's Historic Preservation Office for the specific lot before you plan a renovation, an addition or a teardown.
Deed restrictions. These are private, recorded rules, and in the Heights they are uneven. The City Legal Department's own FAQ notes that "in some Heights area neighborhoods, restrictions are applicable lot by lot". Copies come from the Harris County Clerk. The City's Deed Restriction Enforcement Team can enforce certain recorded restrictions, but it does not give legal advice. Some blocks may also carry minimum building line or minimum lot size rules.
For buyers, the takeaway is to read the title commitment and the recorded restrictions before the option period ends, not after.