Right or wrong?

Legitimacy of the government常理解為「政府本身的合法性」。在此句而言，與「政府在法律上可否興建更多堆填區」沒有關係。小心句子之邏輯 - legitimacy純粹是關於construction of more landfill sites，固建議如下：It is a legitimate strategy for the government to construct more landfill sites.或The Government claims its legitimacy regarding the constructions of more landfill sites.或The Government is perfectly legal regarding the constructions of more landfill sites.

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Incorrect.

You may think Legitimacy measn legally or being legal. But the word does not work like what you think in a sentence or as a term refer to as being legal.

I will say:

The government only need to work within the law to increase the landfill site construction.政府只是按現有法例便可進行堆填區擴建。

Legitimacy is a noun, so if you really want to use this word, you may have to write as follows:

The legitimacy for more landfill construction by the government is already in the law.政府要增加堆填區的法理已經寫在法律內。

Or use the word as adjactive, Legitimate

It is legitimate for the government to construct more landfill by the current law.在現行法例下政府是「有權」擴建堆填區的。

What do you want to say? I am afraid that the word 'legitimacy' is not appropriate.

The sentence is grammatically correct, but I think the idea of it is a bit strange. I think using "approval" instead of "legitimacy" is more suitable.