terminal-start-contribution.ts

import { injectable, inject } from 'inversify';
import { FrontendApplicationContribution, FrontendApplication } from '@theia/core/lib/browser';
import { FrontendApplicationStateService } from '@theia/core/lib/browser/frontend-application-state';
import { TerminalService } from '@theia/terminal/lib/browser/base/terminal-service';
import { TerminalWidget } from '@theia/terminal/lib/browser/base/terminal-widget';

@injectable()
export class TerminalStartContribution implements FrontendApplicationContribution {

    @inject(FrontendApplicationStateService)
    protected readonly stateService: FrontendApplicationStateService;

    @inject(TerminalService)
    protected readonly terminalService: TerminalService;

    protected readonly TERMINAL_ID = 'start:terminal:id'

    async onStart(app: FrontendApplication): Promise<void> {

        this.stateService.reachedState('ready').then(
            async () => {
                // Determine if a terminal currently exists, else skip.
                if (this.terminalService.getById(this.TERMINAL_ID)) {
                    return;
                }
                // Create a new terminal, start it and activate it.
                const terminal = await this.createTerminal();
                await terminal.start();
                this.terminalService.activateTerminal(terminal);
            }
        );
    }

    protected async createTerminal(): Promise<TerminalWidget> {
        const terminal = await this.terminalService.newTerminal({
            id: this.TERMINAL_ID,
            title: 'Vince',
            destroyTermOnClose: true,
            useServerTitle: false,
        });
        return terminal;
    }
}

Update:

On line 29: activateTerminal() no longer exists in terminalService.
Instead, use open():

this.terminalService.open(terminal);