It will be obvious when you start casting the spell
Hold Person has the full triad of components; Verbal, Somatic, and Material. As defined by the general rules for casting a spell, these components are fairly obvious:
Verbal (V)
Most spells require the chanting of mystic words. The words themselves aren't the source of the spell's power; rather, the particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion. Thus, a character who is gagged or in an area of silence, such as one created by the silence spell, can't cast a spell with a verbal component.
Somatic (S)
Spellcasting gestures might include a forceful gesticulation or an intricate set of gestures. If a spell requires a somatic component, the caster must have free use of at least one hand to perform these gestures.
Material (M)
Casting some spells requires particular objects, specified in parentheses in the component entry. A character can use a component pouch or a spellcasting focus (found in “Equipment”) in place of the components specified for a spell. But if a cost is indicated for a component, a character must have that specific component before he or she can cast the spell.
At the point at which you want to cast hold person, you will have to start chanting mystic words, making some sort of forceful or intricate gestures with at least one hand, and you will have to pull out and manipulate a small piece of iron or else a spellcasting focus like a wand or other tool appropriate to your class, and it will be pretty obvious when you do so. Even for the verbal component, "mystic words" is obviously not meant to mean normal speech (though some GMs/tables occasionally interpret spells with verbal components that way when it is thematically appropriate, such as for the Suggestion).
It's not possible for you to somehow surreptitiously cast a spell like hold person as part of a speech, unless you have some other ability which allows you to cast hold person without components or obviates your need for spell components generally. For example, a 20th level druid's archdruid class feature states that:
... you can ignore the verbal and somatic components of your druid spells, as well as any material components that lack a cost and aren’t consumed by a spell.
Such a character could cast a spell without any outward signs at all, and nothing seems to preclude them holding a conversation while they do it (I would assume any 20th level caster has had plenty of practice concentrating while multi-tasking).