der Draht
wire
A thin, long, and bendable strand of metal. It is used, for example, for electrical cables, fences, or crafts.
Der Zaun wurde mit einem stabilen Draht repariert.
The fence was repaired with a sturdy wire.

wire
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wire
A thin, long, and bendable strand of metal. It is used, for example, for electrical cables, fences, or crafts.
Der Zaun wurde mit einem stabilen Draht repariert.
The fence was repaired with a sturdy wire.

In the idiom 'einen Draht zu jemandem haben' (to have a good connection with someone), the person with whom you have a good relationship is always in the dative. So the question is: 'Zu wem hast du einen guten Draht?' (Who do you have a good connection with?)
Er hat einen guten Draht zu seinen neuen Kollegen.
He has a good connection with his new colleagues.
The idiom 'die Drähte ziehen' (to pull the strings) is always used in the plural. If you hear 'Drähte' in connection with power or control, this figurative meaning is intended.
Man vermutet, dass einflussreiche Geschäftsleute im Hintergrund die Drähte ziehen.
People suspect that influential businesspeople are pulling the strings in the background.
The expression 'auf Draht sein' (to be on the ball) is colloquial. It is mostly used in informal conversations to express that someone is attentive and capable.
Ich brauche morgens erst einen Kaffee, um richtig auf Draht zu sein.
I need a coffee in the morning first to really be on the ball.
In the literal sense, 'Draht' (wire) is often combined with verbs like 'spannen' (to stretch), 'verlegen' (to lay/install), 'durchschneiden' (to cut through), or 'biegen' (to bend). Common compounds are 'Stacheldraht' (barbed wire) or 'Kupferdraht' (copper wire).
Der Elektriker hat einen neuen Draht für die Lampe verlegt.
The electrician installed a new wire for the lamp.
connection / association
'die Verbindung' and 'der Draht' can both mean a good relationship with a person. 'Verbindung' is neutral and can describe a social or professional contact that is useful. 'einen guten Draht zu jemandem haben' (to have a good connection with someone) is a fixed expression. It sounds more personal and somewhat more colloquial. It means that you get along well with someone or have easy access to that person. The words can be confused because both can describe contacts. For general contacts, 'Verbindung' fits. For a good personal relationship, 'ein guter Draht' is appropriate.

Frau Hofmann hat einen guten Draht zu den neuen Kollegen.
Ms. Hofmann has a good connection with the new colleagues.
Durch seine Verbindung zur Behörde bekam Herr Kaya schnell die nötige Auskunft.
Through his connection to the authority, Mr. Kaya quickly got the information he needed.