As @pcoz mentioned it is answering the point made in the previous pasuk which asks:
מִֽי־יַעֲלֶ֥ה בְהַר־יְהֹוָ֑ה וּמִי־יָ֝קוּם בִּמְק֥וֹם קׇדְשֽׁוֹ
Who may ascend the mountain of the LORD? Who may stand in His holy place?
According to the Metzudos Dovid the initial requirement is that there is a need to be first a man of upright integrity, and that means his actions must be clean of any unlawful gain. He writes there:
נקי כפים. וכאלו השיב זהו הראוי מי שכפיו נקיים מממון שאינו של יושר ולבו ברור ביראת ה׳ ולא מפחד אדם
Clean hands - And it is as if he is replying that it is fitting for one whose hands are clean from money/wealth that is not of honesty and whose heart is clear in the fear of G-d and not afraid of man.
Rav Shimshon Raphael Hirsch observes that the word "כף" literally mean "palm" as this is what firmly takes hold of an object. Therefore, the righteous man who is painted in this context, does not hold on to something gained through any dishonest or unscrupulous dealings.
Thus, to answer your questions the first prerequisite here is to get one's actions correct and only then the natural progression of thought and speech follows.
It is worth noting parenthetically that Radak makes a similar observation.
Radak analyses these three stages of action, thought and speech, and writes as follows:
The clean of hand and pure of heart, who hath not lifted up his soul unto vanity, And hath not sworn deceitfully: – Notice that he indicates in this verse three dispositions in man, action, thought, and speech; and in the three of them the man will be perfect who shall be clean in his actions, pure in his heart, and trustworthy in his speech. (The marginal reading) is נפשׁי (written) with yodh ( = my soul), and is the utterance of God, as (in the verses) (Exod. 20:7; Deut. 5:11), "Thou shalt not take the name of the Lord thy God in vain"; and נפשׁו (His soul, essence, being) is (equivalent to) His Name. And so it says (in the verse) (Amos. 6:8), "The Lord God hath sworn by Himself (בנפשׁו)." And the word as written, נפשׁו, i.e. with waw, means his soul, viz. the swearer's; a man shall not lift up unto vanity nor swear deceitfully, but in truth and righteousness. And such swearing is a mitzvah to the fearers of the Name, as is said (in the text) (Deut. 6:13), "And shalt swear by His Name"; and another verse says (ibid. 10:20), "The Lord thy God shalt thou fear, Him shalt thou serve, and to Him shalt thou cleave, and by His Name shalt thou swear." When these attributes (i.e. service, fear, adhesion) are thine, then by His Name shalt thou swear. And so it says (Jer. 4:2), "And thou shalt swear 'As the Lord liveth,' in truth, in judgment, and in righteousness." (Sefaria translation my emphasis)