Meaning
An instruction to go slowly, be careful, or handle something gently. Broader than English 'take your time', 'tek time' can mean 'be careful', 'ease up', or 'handle it softly' as much as 'don't rush' — 'tek time wid di baby' is handle the baby gently, 'tek time pon di road' is drive carefully. It counsels care, patience, and a gentle hand, and it carries the folk wisdom that hurrying and roughness bring trouble, while 'tek time' brings things safely through.
Examples
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Tek time wid di glass dem, dem a bruk easy.
Be careful with the glasses, they break easily.
Here 'tek time' means 'handle carefully', not 'go slow'; 'dem' pluralises 'glass'.
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Tek time drive, di road slippery.
Drive carefully, the road is slippery.
No copula before 'slippery' — 'di road slippery' not 'the road is slippery'.
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Tek time, nuh badda rush yuhself.
Slow down, don't rush yourself.
'Badda' means 'bother'; 'nuh badda' is a soft prohibition, 'don't bother to'.
Origin
From English 'take time', with the sense of care and caution expanded well beyond the standard meaning of merely not hurrying.
How it’s used
Very common and warm in tone; often said protectively by an elder or friend. Foreigners hearing only 'go slow' miss the 'be careful' sense that is often intended.