I suspect that in 1890 H.M. may be Her Majesty's but C. might be Customs, Commissioner, Cutter or something else.
The asker commented:
I found Sands dir's in Ancestry. Found no list of abbr'ns there. I
searched Trove newspapers for Henry Gill. Found other names in Sands
with "HMC" and searched Trove for their names hoping to see what HMC
means. Looked in Govt gazettes on Trove for Customs Dept staff
appointments. I found there a Henry Gill on Customs Dept staff around
the same time, though no guarantee it's same person. There wasn't much
alignment of Customs apptmts to Sands HMC entries.
I looked for lists of abbreviations for Sands directories without success too.
I think the asker finding a Henry Gill amongst Customs Department staff around the same time as the Sands directory entry makes a good case for H.M.C. being an abbreviation for Her Majesty's Customs.