The plural abbreviation for government is govts. You can abbreviate the word government as government. On a business card or on a nameplate. It is also common to see these types of abbreviations in headlines or titles of newspapers where space is a concern.
The capitalization and score of the government abbreviation may differ, but not much. For example, Govt, Govt. Abbreviation for Oxford Advanced American Dictionary. An official website of the United States Government Use of official websites.
gov A. gov belongs to an official government organization in the United States. This abbreviation is usually found in reference to any structured governing body of a given nation when shorthand notes are taken and in many other cases, since it is an almost universally recognized abbreviation. The applications of this abbreviation in everyday conversations within the English language are far from common.
None of the various sources I consulted recommend the abbreviation gov't; instead, they divide their preferences by govt. Although I'm not sure at all that supports this, I would suggest that the inclusion of t is possibly more common (in the UK), and that the abbreviation gov. I have always understood that the conventional practice of whether to include a period at the end of an abbreviation is to include one if the last letter of the entire word is not present in the abbreviation, and not to include one if it is present. You may want to abbreviate the word “government” if you are writing a document, text, or notes, but it can be confusing to know the correct way to abbreviate the word.
My choice to capitalize the initial letter of the abbreviation would follow exactly if I would capitalize the initial letter of the entire word in the respective context.