export interface ITooltip {
    new(elem: HTMLElement, options?: ITooltipOptions);
    show(): void;
    hide(): void;
    toggle(): void;
}

export class Tooltip implements ITooltip {

    constructor(private  elem: HTMLElement, private options?: ITooltipOptions) {
    }

    ....
}

Class 'Tooltip' incorrectly implements interface 'ITooltip'.
  Type 'Tooltip' provides no match for the signature 'new (elem: HTMLElement, options?: ITooltipOptions): any'